Decomposing hypergraphs into k-colorable hypergraphs

For a given hypergraph H with chromatic number \chi(H) and with no edge containing only one vertex‎, ‎it is shown that the minimum number l‎ ‎for which there exists a partition (also a covering) \{E_۱,E_۲,\ldots,E_l\} for E(H)‎, ‎such that the hypergraph induced by‎ ‎E_i for each ۱\leq i\leq l is k-colorable‎, ‎is \lceil‎ ‎\log_{k} \chi(H) \rceil‎.

Keywords:

‎Hypergraph‎ , ‎Chromatic number‎ , ‎k-Colorable